Finite Element Analysis of X-Ray Targets

A. Plankensteiner, P. Rödhammer RM 2 21
250mm diameter (see Fig.4). These stresses cause plastic strains at the inner
diameter of T250 that lie in the same range as those obtained under electron beam
exposure (see Fig.12). Note that the criticality of increased rotational frequencies is
borne out already at present designs and loading conditions, with a dramatic increase
in failure rates during tube operation being observed upon an increase of the rotational
frequency e.g. from 120Hz to 150Hz.
The evolution of the focal temperatures (= 2D-averaged surface temperature at the
midpoint of the track width) under an electron beam exposure of 100kW is shown in
Fig.6. The maximum of ~1750°C attained after 10 sec (for T190) and after 30 sec (for
T250) is compatible with the temperature spike in the focal spot to be superposed.
During the 600 sec pause time (not shown) the anodes cool down to starting
temperatures of 500 – 600°C. In cyclic operation final temperatures may be expected
to reach an upper limit around 1900°C. As obvious from Fig.6 anode T250 holds a
large temperature threshold when operated at 100kW/10sec cycles.
The cross-sectional distributions of temperatures (Fig.5) show pronounced
temperature gradients between the hot outer section and the cooler inner section. For
T250 the gradient appears steeper after the 10sec exposure than after the 30sec
exposure. As discussed below, these gradients induce severe radial stresses in the
target via differential thermal expansion.
At the end of exposure superposition of centrifugal forces and temperature-induced
stresses generate stress levels that in some areas of the cross-section are well beyond
the yield strength at the respective temperatures (see Figs. 8 and 9). In particular the
area around the inner radius is put under severe tensile stress under the pulling action
of the hot outer ring. As to be expected the situation is most critical for target T250
operating at 250Hz. Note that local stress levels might be even higher in transient
states with more unfavourable temperature distributions (e.g. steeper gradients).
During cool-down the outer region of the anodes goes into a state of tensile stress (see
Figs. 9 and 10). Below the focal track stresses in the TZM rise up to the range of
250MPa, discomfortingly high in view of the thermo-shock loading of the focal track
and possible crack formation in the latter.
At the end of exposure plastic straining has occurred for both designs and under all
loading conditions (see Figs. 11 and 12). The accumulated plastic strains are on the
order of 1%, and for a given design are increasing with frequency and exposure time.
Additional plastic straining occurs during cool-down of the anodes in the outer regions,
whereas the inner section remains unaffected (see Figs. 13 and 14).